In a large bowl, whisk together flour, sugar, and salt. Whisk together egg, water, and vinegar. Keep in fridge.
Add the cubed butter and shortening and work into the flour using a pastry cutter. When it resembles peas, add the cold liquid. Switch to wooden spoon and mix until it just comes together.
Divide the dough in half and wrap in plastic wrap. Chill for at least 30 minutes. You can freeze the other half for another time.
While the crust is chilling, you can get started on the filling. Cook the bacon until crisp. Remove the bacon from the pan, leaving about 1 Tablespoon fat in the pan. Pour off any remaining. Let the bacon drain on paper towels.
Add green onions, peppers, and corn to the pan. Season with salt and pepper. Cook until slightly soft, about 4 to 5 minutes. Let cool slightly.
Roll out the pie crust on a floured board. Roll into a circle and transfer to a pie plate. Trim the crust, tuck under, and crimp.
Add the cooled corn filling to the pie crust. Top with fresh basil and cheeses.
To make the custard, add the eggs to a blender or large measuring bowl (I use a batter bowl). Pour in cream or half-and-half, salt, pepper, nutmeg, and cayenne. Blend until frothy, about 2 minutes.
Pour custard over. Let sit for minute and use a fork to make sure everything is evenly distributed.
Place quiches on a rimmed baking sheet (for insurance in case you get any spill over) and cover loosely with foil.
Bake in a preheated 400° for 45 minutes, remove foil and bake for another 10 minutes. Let stand for 15 minutes before slicing.